Question

The number of numbers formed having not more than $6$ digits using the numbers $3,4,5$ when repetition is allowed is

• A. $1092$
• B. $1090$
• C. $1085$
• D. $1064$

Answer 1

The correct option is A $1092$

No of 1 digit no's $=\_\to 3\left(Possibilities\right)$

No of 2 digit no's $=\_\_\to 3\times 3=9$

No of 3 digit no's $=\_\_\_\downarrow \downarrow \downarrow 333\to 3\times 3\times 3=27$

No of 6 digit no's $=\_\_\_\_\_\_\downarrow \downarrow \downarrow \downarrow \downarrow \downarrow 333333=3^6$

$\therefore$ Total $=3+3^2+3^3+3^4+3^5+3^6=1092$